# Ex.13.1 Q1 Direct and Inverse Proportions Solution - NCERT Maths Class 8

## Question

Following are the car parking charges near a railway station up to:

\(4\) hours ₹\(60\)

\(8\) hours ₹\(100\)

\(12\) hours ₹\(140\)

\(24\) hours ₹\(180\)

Check if the parking charges are in direct proportion to the parking time.

## Text Solution

**What is Known?**

Parking charges for different hours.

**What is Unknown?**

Parking charges are direct proportion to the parking time or not.

**Reasoning:**

If two quantities are related in such a way that an increase in one lead to a corresponding proportional increase in the other, then such a variation is called direct variation.

**Steps:**

The parking charge for \(1\) hour in all the four cases then the variation is direct.

We have:

\[\begin{align}\frac{{60}}{4}&=\frac{{15}}{1}\\&=15\\ \\ \frac{{100}}{8}&=\frac{{25}}{2}\\ &= 12.5\\ \\ \frac{{140}}{{12}} &=\frac{{35}}{3}\\&=11.67 \\ \\\frac{{180}}{{24}}&=\frac{{15}}{2}\\&= 7.50\end{align}\]

Since all the values are not the same, the parking charges are not in direct proportion to parking times.